Dice Decision

Yahtzee Dice 3, 3, 3, 5, 6: What Should You Keep?

A detailed breakdown of the optimal strategy for one of the most common Yahtzee dice decisions

Published February 6, 20265 min readStrategy

If you rolled 3, 3, 3, 5, 6 in Yahtzee, the best play is usually to keep 3, 5, 6 and go for a Straight (expected value ~21 points) rather than keeping three 3s (expected value ~17 points). However, the optimal choice depends on which categories are still open on your scorecard.

Quick Answer: Keep 3, 5, 6 if you still need a Large Straight (40 pts) or Small Straight (30 pts) — the expected value is ~21 points. Keep three 3s if Straights are already filled, or you need 3s for the upper section bonus — expected value is ~17 points. Full probability breakdown below.

Option 1: Keep Three 3s (Reroll the 5 and 6)

Keeping three 3s gives you a guaranteed 9 points in the 3s category. But you're really hoping to improve to Four of a Kind, Full House, or even Yahtzee.

Possible Outcomes

  • Yahtzee (3-3-3-3-3): Worth 50 points — probability ~2.8%
  • Four 3s (3-3-3-3-X): Score in Four of a Kind for ~15-18 points — probability ~13.9%
  • Full House (3-3-3-X-X): Worth 25 points — probability ~16.7%
  • Three of a Kind (keep 3-3-3): Sum all dice for ~17-21 points
  • Upper Section 3s: Guaranteed minimum 9 points

Expected Value: Approximately 15-20 points depending on open categories

Option 2: Keep 3, 5, 6 (Reroll the two extra 3s)

Keeping 3, 5, 6 means you're going for a Straight. You need a 4 to complete a Large Straight (3-4-5-6-X) or a 2 or 4 for a Small Straight.

Possible Outcomes

  • Large Straight (2-3-4-5-6 or 3-4-5-6-7): Worth 40 points — probability ~13.9%
  • Small Straight (X-3-4-5-6 or 2-3-4-5-X): Worth 30 points — probability ~33.3%
  • Chance: Use the sum of all dice as fallback — typically 18-25 points

Expected Value: Approximately 19-24 points when Straight categories are open

Expected Score Comparison

StrategyBest CaseExpected ValueWorst Case
Keep 3, 3, 350 pts (Yahtzee)~17 pts9 pts (just 3s)
Keep 3, 5, 640 pts (Large Straight)~21 pts~14 pts (Chance)

When both Straight categories are open, keeping 3, 5, 6 has a higher expected value. But when Straights are already filled, keeping three 3s is clearly better.

When Context Matters: Check Your Scorecard

Large Straight and Small Straight are open

Keep 3, 5, 6 — higher expected value targeting 30-40 points

Straights are filled, but 3s/Three of a Kind are open

Keep three 3s — go for Four of a Kind, Full House, or Yahtzee

Need the upper section bonus (63 points)

Keep three 3s — lock in 9 points for 3s (you need 3× each number for the bonus)

Yahtzee category is still open

Consider keeping three 3s — a 2.8% shot at 50 points plus guaranteed fallback options

Late game with few categories left

Pick whichever targets your remaining open categories

Quick Decision Guide

Keep 3, 5, 6 when:

  • Large Straight is still open
  • Small Straight is still open
  • You need high-value points this turn

Keep 3, 3, 3 when:

  • Both Straight categories are filled
  • You need points in the 3s row for the upper bonus
  • Three/Four of a Kind or Full House are open
  • Yahtzee box is still open and you want to gamble

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Yahtzee Dice 3 3 3 5 6: What Should You Keep? | Optimal Strategy